tolkiens legendarium - How did Gandalf get each of his various names?

Gandalf goes by many names in Tolkien's works. Gandalf himself says in The Two Towers:

"Many are my names in many countries. Mithrandir among the elves, Tharkûn to the dwarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf, to the East I go not."

Before leaving Valinor, he only had the one name: Olórin. Do we know what individuals gave him the rest of these names or what events might have triggered them, beyond what is in the above quote alone?

Answer

Not the specifics, unfortunately. Much of what we know comes from Unfinished Tales:

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  Mithrandir

  
  
  

  
  

  [T]he last-comer was named among the Elves Mithrandir, the Grey Pilgrim, for he dwelt in no place, and gathered to himself neither wealth nor followers, but ever went to and fro in the Westlands from Gondor to Angmar, and from Lindon to Lórien, befriending all folk in times of need.

  
  

  ^{Unfinished Tales Part 4 Chapter II: "The Istari"}

  
  

  
  


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  Gandalf

  
  

  
  

  Mostly he journeyed unwearingly on foot, leaning on a staff; and so he was called among Men of the North Gandalf, “the Elf of the Wand”. For they deemed him (though in error, as has been said) to be of Elven-kind, since he would at times works wonders among them, loving especially the beauty of fire; and yet such marvels he wrought mostly for mirth and delight, and desired not that any should hold him in awe or take his counsels out of fear.

  
  

  ^{Unfinished Tales Part 4 Chapter II: "The Istari"}

  
  
  

  
  


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  Incánus I discuss in more detail on another question

  
  


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  Olórin

  
  

  
  

  After the words "But of Olórin we shall never know more than he revealed in Gandalf" my father added later:

  
  

  
  
  

  save that Olórin is a High-elven name, and must therefore have been given to him in Valinor by the Eldar, or be a "translation" meant to be significant to them.

  
  

  
  

  ^{Unfinished Tales Part 4 Chapter II: "The Istari"}

  
  

  
  

He has a few other names that aren't mentioned in the question, but most have similarly vague origins:

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  Greyhame is used exclusively in Rohan. As noted by Wayne Hammond and Christina Scull in A Reader's Companion, this is a modernization of the Old English græghama, which means "grey-coated." This name probably dates back to Gandalf's first appearances in Rohan, since it's the obvious name for him

  
  
  


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  Stormcrow is used mainly in Rohan, but also by Gandalf himself at the borders of Gondor. Although we don't know where this name came from, or who coined it, it's likely that it came about because of the perception of Gandalf as a bearer of bad news (as with Láthspell) below; as one of the Gondorian guards says:

  
  

  
  

  'May you bring good counsel to Denethor in his need, and to us all, Mithrandir!' Ingold cried. 'But you come with tidings of grief and danger, as is your wont, they say.'

  
  

  ^{Return of the King Book V Chapter 1: "Minas Tirith"}

  
  

  
  

In only two cases do we know both the specific individual and the circumstances surrounding the name:

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  Láthspell was probably given by Wormtongue; it's the first we hear of the name, anyway:

  
  

  
  

  Why indeed should we welcome you, Master Stormcrow? Láthspell I name you, Ill-news; and ill news is an ill guest they say.' [Wormtongue] laughed grimly, as he lifted his heavy lids for a moment and gazed on the strangers with dark eyes.

  
  

  ^{The Two Towers Book III Chapter 6: "The King of the Golden Hall"}

  
  

  
  


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  The White Rider was likely coined by Aragorn:

  
  
  

  
  

  'Do I not say truly, Gandalf,' said Aragorn at last, 'that you could go whithersoever you wished quicker than I? And this I also say: you are our captain and our banner. The Dark Lord has Nine. But we have One, mightier than they: the White Rider. He has passed through the fire and the abyss, and they shall fear him. We will go where he leads.'

  
  

  ^{The Two Towers Book III Chapter 5: "The White Rider"}

  
  

  
  

  It's later used by Gandalf himself, the Eorlingas (who learn it from Aragorn), and Pippin (who likely heard it from Aragorn, Legolas, or Gimli after the Battle of Helm's Deep)

  
  

Unfortunately, that's the most we know about how these names came to be applied to Gandalf. The specific circumstances, and the first individuals to use each name, is unrecorded.